Searching for Repeating Ground Track Orbits: A Systematic Approach
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Searching for Repeating Ground Track Orbits: A Systematic Approach 1 Martin Lara' Abstract For the zonal part of the Earth artificial satellite problem, families of periodic orbits are computed in a synodic reference frame. A systematic procedure for finding periodic orbits at any inclination is described. The solutions found in this way are frozen orbits that repeat their ground track exactly on the surface of the Earth and are a very good start for further refinements including other perturbations. A practical application is provided.
Introduction In reference to mission planning for artificial satellites, the search for orbits that retrace their ground tracks on the surface of the Earth is an important problem. "Repeating ground track" configurations may be highly desirable for missions related to Earth surveillance or for constellations of communication satellites. Ideal conditions for these repeating ground track orbits will be those corresponding to orbits that are periodic in a rotating frame attached to the Earth. A method for finding polar orbits that are periodic in a rotating frame attached to the Earth is discussed in [1] where a zonal model was considered for the potential. In that paper, tools designed to deal with dynamical systems with two degrees of freedom were used to compute the family of polar periodic orbits for variations of the energy in the inertial frame. Several of the orbits pertaining to that family were shown to be also periodic in a rotating frame attached to the Earth. The last situation occurs when the frequency of the satellite in the polar periodic orbit is commensurable with the rotation rate of the Earth. In the present communication, the method given in [1] is extended to consider orbits at any inclination, not just the polar case, and a systematic approach is proposed for assisting mission designers in their procedures for searching for repeating ground track configurations. Since the repeat orbits constructed with the technique proposed 'Presented at the AAS/AIAA Spaceflight Mechanics Meeting, Monterey, California, February, 1998. Cdr. of the Spanish Navy. Real Instituto y Observatorio de la Armada, 11110 San Fernando (SPAIN).
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in this paper are periodic in the rotating meridian plane of the satellite, they are also frozen orbits (see [3]), meaning the argument of perigee and eccentricity are fixed in inertial space. The scheme provided here is based on the computation of families of periodic orbits for conservative dynamical systems with either two or three degrees of freedom. A vectorial formulation of the predictor-corrector algorithm given in [2] is used to that effect. The procedure is based on the numerical integration of the equations of motion jointly with the linear variations. A brief description of the predictor-corrector algorithm is given in the paper. The potential model used for the computations considers the zonal part of the Earth artificial satellite problem, where harmonic coefficients J 2 through J 9 have been taken into account. T
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